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The Ultimate Guide to Percentages

What is a Percentage?

The word "percentage" comes from the Latin per centum, which literally means "by the hundred." In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Percentages are used to express how large or small one quantity is relative to another quantity. For example, if you have 50 apples and 10 of them are red, then 20% of your apples are red.

Common Percentage Formulas

There are three main types of percentage problems you might encounter. Our calculator handles all of them:

  1. Finding the percentage of a number:
    Formula: Value = (Percentage / 100) × Total
    Example: What is 20% of 150? (0.20 × 150 = 30)
  2. Finding what percentage one number is of another:
    Formula: Percentage = (Value / Total) × 100
    Example: 30 is what percent of 150? (30 / 150 = 0.2; 0.2 × 100 = 20%)
  3. Finding the total when you know the percentage and the value:
    Formula: Total = Value / (Percentage / 100)
    Example: 30 is 20% of what number? (30 / 0.20 = 150)

Real-World Applications

Percentages are everywhere in our daily lives. Understanding them is crucial for:

  • Shopping: Calculating discounts (e.g., "25% off") and sales tax.
  • Finance: Understanding interest rates on loans, credit cards, and savings accounts.
  • Business: Calculating profit margins, growth rates, and market share.
  • Health: Reading nutrition labels (e.g., "% Daily Value") and understanding medical statistics.
  • Statistics: Interpreting poll results, sports data, and scientific research.

Percentage Increase and Decrease

Percentage change is used to describe the relative change between an old value and a new value. It is calculated as:

((New Value - Old Value) / |Old Value|) × 100

If the result is positive, it's a percentage increase. If negative, it's a percentage decrease.

Tips for Mental Math

  • 10% Rule: To find 10% of any number, just move the decimal point one place to the left.
  • 5% Rule: Find 10% and then divide by 2.
  • 20% Rule: Find 10% and then multiply by 2.
  • 1% Rule: Move the decimal point two places to the left.

Frequently Asked Questions

To convert a fraction to a percentage, divide the numerator by the denominator and then multiply the result by 100. For example, 3/4 = 0.75; 0.75 × 100 = 75%.

A percentage is a number out of 100. A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations falls. For example, if you are in the 90th percentile, you scored better than 90% of the group.

To calculate a 20% tip, multiply your total bill by 0.20. Alternatively, find 10% (move decimal one place left) and double it.

Yes! A percentage greater than 100 means the value is more than the original total. For example, 200% of 50 is 100. This often happens in growth rates or price increases.

Subtract the new value from the old value, divide by the old value, and multiply by 100. For example, if a price drops from $100 to $80: (100-80)/100 = 0.2; 0.2 × 100 = 20% decrease.

Math Tips

  • "Of" usually means multiply in math.
  • "Is" usually means equals.
  • Always convert % to decimal for math.
  • Check if your answer makes sense.
  • Use our calculator for complex decimals!

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Disclaimer

While we strive for 100% accuracy, this calculator is for educational and informational purposes only. Always double-check important financial or scientific calculations manually or with a professional.